Question: Simplify the following expression: $z = \dfrac{r^2 + r - 42}{r - 6} $
Solution: First factor the polynomial in the numerator. $ r^2 + r - 42 = (r - 6)(r + 7) $ So we can rewrite the expression as: $z = \dfrac{(r - 6)(r + 7)}{r - 6} $ We can divide the numerator and denominator by $(r - 6)$ on condition that $r \neq 6$ Therefore $z = r + 7; r \neq 6$